GATE | GATE-CS-2015 (Set 2) | Question 51

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates x_a and x_b for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(x_b) is very small and then x_b is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method? Secant

Initialize: x_a, x_b, ε, N     // ε = convergence indicator
f_b = f(x_b) i = 0
while (i < N and |f_b| > ε) do
   i = i + 1                 // update counter
   x_t = ?                    // missing expression for
                             // intermediate value
   x_a = x_b                   // reset x_a
   x_b = x_t                   // reset x_b
   f_b = f(x_b)                // function value at new x_b
end while
if |f_b| > ε
  then // loop is terminated with i = N
  write “Non-convergence”
else
  write “return x_b”
end if

(A)

x_b – (f_b– f(x_a)) f_b/ (x_b – x_a)

(B)

x_a– (f_a– f(x_a)) f_a/ (x_b – x_a)

(C)

x_b – (f_b – x_a) f_b/ (x_b – f_b(x_a)

(D)

x_a – (x_b – x_a) f_a/ (f_b – f(x_a))

Answer

Please comment below if you find anything wrong in the above post
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